Space-time Trajectories Research Articles

Relativistic Bohmian trajectories of photons via weak measurements

Bohmian mechanics is a nonlocal hidden-variable interpretation of quantum theory which predicts that particles follow deterministic trajectories in spacetime. Historically, the study of Bohmian trajectories has mainly been restricted to nonrelativistic regimes due to the widely held belief that the theory is incompatible with special relativity. Here, we present an approach for constructing the relativistic Bohmian-type velocity field of single particles. The advantage of our proposal is that it is operational in nature, grounded in weak measurements of the particle’s momentum and energy. We apply our weak measurement formalism to obtain the relativistic spacetime trajectories of photons in a Michelson–Sagnac interferometer. The trajectories satisfy quantum-mechanical continuity and the relativistic velocity addition rule. We propose a modified Alcubierre metric which could give rise to these trajectories within the paradigm of general relativity.

Topological orders, braiding statistics, and mixture of two types of twisted BF theories in five dimensions

Topological orders are a prominent paradigm for describing quantum many-body systems without symmetry-breaking orders. We present a topological quantum field theoretical (TQFT) study on topological orders in five-dimensional spacetime (5D) in which topological excitations include not only point-like particles, but also two types of spatially extended objects: closed string-like loops and two-dimensional closed membranes. Especially, membranes have been rarely explored in the literature of topological orders. By introducing higher-form gauge fields, we construct exotic TQFT actions that include mixture of two distinct types of BF topological terms and many twisted topological terms. The gauge transformations are properly defined and utilized to compute level quantization and classification of TQFTs. Among all TQFTs, some are not in Dijkgraaf-Witten cohomological classification. To characterize topological orders, we concretely construct all braiding processes among topological excitations, which leads to very exotic links formed by closed spacetime trajectories of particles, loops, and membranes. For each braiding process, we construct gauge-invariant Wilson operators and calculate the associated braiding statistical phases. As a result, we obtain expressions of link invariants all of which have manifest geometric interpretation. Following Wen’s definition, the boundary theory of a topological order exhibits gravitational anomaly. We expect that the characterization and classification of 5D topological orders in this paper encode information of 4D gravitational anomaly. Further consideration, e.g., putting TQFTs on 5D manifolds with boundaries, is left to future work.

Distribution analysis method of key targets based on big data analysis engine for maritime space-time trajectory

Abstract Now a large amount of maritime space-time trajectory data has been collected, but its deep value is unable to be tapped, and the analysis of the distribution of key targets has also encountered bottlenecks. The emergence of big data technology provides us with a solution. This paper proposes a big data analysis engine for maritime space-time trajectory, which makes full use of the data characteristics and improves the overall computing performance of the engine. Based on this engine, a dispersal analysis algorithm for key military targets at sea is proposed to achieve rapid retrieval and dispersal analysis of key marine targets. It has been tested and verified that this engine has excellent performance and can become an efficient query and analysis engine for maritime space-time trajectory data. The key target distribution analysis algorithm has certain research significance and practical value.

Multi-rhythm control for heterogeneous traffic and road networks in CAV environments

Heterogeneity is widely observed in various aspects of urban transport, such as road types, vehicle dynamics, and demand patterns, which greatly complexifies transport systems and hinders the successful control and management of traffic. On one hand, intelligent strategies are required to relieve the loss of efficiency caused by the mixed traffic flow composed of vehicles with different speeds; on the other hand, the spatial heterogeneity of travel demand distribution requires pertinent control schemes to improve the network-level mobility and the phenomenon of oversaturation under heavy traffic also demands an appropriate way to resolve. Leveraging the advantages of connected and automated vehicle (CAV) technology, this study proposes a multi-rhythm control (MRC) scheme to accommodate heterogeneous network traffic in a CAV environment with 100% penetration rate. While the rhythmic control (RC) proposed by (Lin et al., 2021) could organize traffic efficiently and in an orderly manner, the multi-rhythm strategy has greater potential to not only improve the efficiency of heterogeneous traffic by the design of different virtual platoons (VPs) catering to different vehicle types, but also address the spatial heterogeneity of network traffic by implementing differentiated cycle lengths among the road network. For the optimal design of the MRC scheme, a two-step model is developed to minimize the total travel cost, where the first step focuses on the mesoscopic level to jointly optimize the multi-rhythm scheme, VP design and lane configuration for both undersaturated and oversaturated cases, while the second step focuses on the microscopic design to optimize the space–time trajectories of VPs under the premise of collision free. Numerical examples and simulation experiments are conducted to test the performances of the MRC scheme compared to a naive version of RC with a homogeneous rhythm and a traffic signal control (TSC) strategy. The results show that among all control strategies, the MRC scheme has the best performance under all kinds of demand patterns, which is reflected in both the lowest travel cost and the highest network throughput.

Relativistic Langevin equation derived from a particle-bath Lagrangian

We show how a relativistic Langevin equation can be derived from a Lorentz-covariant version of the Caldeira–Leggett particle-bath Lagrangian. In one of its limits, we identify the obtained equation with the Langevin equation used in contemporary extensions of statistical mechanics to the near-light-speed motion of a tagged particle in non-relativistic dissipative fluids. The proposed framework provides a more rigorous and first-principles form of the weakly-relativistic and partially-relativistic Langevin equations often quoted or postulated as ansatz in previous works. We then refine the aforementioned results to obtain a generalized Langevin equation valid for the case of both fully-relativistic particle and bath, using an analytical approximation obtained from numerics where the Fourier modes of the bath are systematically replaced with covariant plane-wave forms with a length-scale relativistic correction that depends on the space-time trajectory in a parabolic way. A new relativistic force term appears in this fully-relativistic limit, which has been derived here for the first time. We discuss the implications of the apparent breaking of space-time translation and parity invariance, showing that these effects are not necessarily in contradiction with the assumptions of statistical mechanics. The intrinsically non-Markovian character of the fully relativistic generalised Langevin equation derived here, and of the associated fluctuation–dissipation theorem, is also discussed.

Approach for Topography-Dependent Clutter Suppression in a Spaceborne Surveillance Radar System Based on Adaptive Broadening Processing

In this letter, a novel method is proposed to suppress the terrain fluctuation clutter based on adaptive broadening processing. In the proposed algorithm, the flat interference phase is first compensated according to the priori radar system parameters. Then, according to the space-time trajectory distribution of clutter edge, the level of clutter Doppler spread in virtue of crab effect is estimated by a cost function related to the clutter eigenvector matrix. Finally, after calculating the clutter suppression weight vector according to the broadened clutter subspace, the non-stationary ground clutter can be robustly rejected. The validity of the proposed method is verified by both the simulated and real-measured multichannel radar data.

Crossover scaling functions in the asymmetric avalanche process

We consider the particle current in the asymmetric avalanche process on a ring. It is known to exhibit a transition from the intermittent to continuous flow at the critical density of particles. The exact expressions for the first two scaled cumulants of the particle current are obtained in the large time limit t → ∞ via the Bethe ansatz and a perturbative solution of the TQ-equation. The results are presented in an integral form suitable for the asymptotic analysis in the large system size limit N → ∞. In this limit the first cumulant, the average current per site or the average velocity of the associated interface, is asymptotically finite below the critical density and grows linearly and exponentially times power law prefactor at the critical density and above, respectively. The scaled second cumulant per site, i.e. the diffusion coefficient or the scaled variance of the associated interface height, shows the O(N −1/2) decay expected for models in the Kardar–Parisi–Zhang universality class below the critical density, while it is growing as O(N 3/2) and exponentially times power law prefactor at the critical point and above. Also, we identify the crossover regime and obtain the scaling functions for the uniform asymptotics unifying the three regimes. These functions are compared to the scaling functions describing crossover of the cumulants of the avalanche size, obtained as statistics of the first return area under the time space trajectory of the Vasicek random process.

Architecture of a self-fragmenting droplets cascade.

We report quantitative imaging experiments describing the three-dimensional (3D) bursting cascade of droplets from a liquid melt reacting with the oxygen of air which explode sequentially to produce ever smaller fragments. The 3D space-time resolved trajectories of the fragmenting drops reveal an arborescent structure of branchings defining the cascade steps, each random in direction and shortening along the cascade, in a way we determine. The phenomenon is a unique and prototypical illustration of the so-called Richardson regime, namely, an accelerated cascade towards smaller scales. The phenomenon, which coincides with the early time dispersion period of a Brownian motion, featuring here ever shrinking steps, is well captured by a Langevin dynamics.

Analytical study of light ray trajectories in Kerr spacetime in the presence of an inhomogeneous anisotropic plasma

We calculate the exact solutions to the equations of motion that govern the light ray trajectories as they travel in a Kerr black hole’s exterior that is considered to be filled with an inhomogeneous and anisotropic plasmic medium. This is approached by characterizing the plasma through conceiving a radial and an angular structure function, which are let to be constant. The description of the motion is carried out by using the Hamilton–Jacobi method, that allows defining two effective potentials, characterizing the evolution of the polar coordinates. The elliptic integrals of motion are then solved analytically, and the evolution of coordinates is expressed in terms of the Mino time. This way, the three-dimensional demonstrations of the light ray trajectories are given respectively.

Sensor location design for interdicting mobile travelers with probabilistic space-time trajectories

Most existing sensor location design studies focus on stationary or deterministic objects (e.g., fixed OD demand) yet have not well investigated uncertain mobility of inspected objects. To bridge this gap, this study aims to integrate human mobility characteristics specified by the time geography theory into sensor location design. We first investigate trajectories of moving objects to see how they can reveal detailed information about human travel characteristics and presence probability with high-resolution detail. Then, a space–time network-based modeling framework is proposed to integrate human mobility into network location design problems. We construct a probabilistic network structure to quantify human’s presence probability at different locations and time. Then, a Mixed Integer Nonlinear Programming (MINLP) model is proposed to maximize the spatial and temporal coverage of individual targets. To obtain near optimal solutions for large-scale problems, greedy heuristic, simulated annealing and Lagrangian relaxation algorithms are tested. Theoretical analysis is conducted to show the optimality gap of the greedy algorithm. The proposed algorithms are implemented on hypothetical and real-world numerical examples (some on a high-performance computing platform) to demonstrate the performance and effectiveness of the proposed model on different network sizes and promising results have been obtained.

Neural Network Reconstruction of Plasma Space-Time

We explore the use of Physics-Informed Neural Networks (PINNs) for reconstructing full magnetohydrodynamic solutions from partial samples, mimicking the recreation of space-time environments around spacecraft observations. We use one-dimensional magneto- and hydrodynamic benchmarks, namely the Sod, Ryu-Jones, and Brio-Wu shock tubes, to obtain the plasma state variables along linear trajectories in space-time. These simulated spacecraft measurements are used as constraining boundary data for a PINN which incorporates the full set of one-dimensional (magneto) hydrodynamics equations in its loss function. We find that the PINN is able to reconstruct the full 1D solution of these shock tubes even in the presence of Gaussian noise. However, our chosen PINN transformer architecture does not appear to scale well to higher dimensions. Nonetheless, PINNs in general could turn out to be a promising mechanism for reconstructing simple magnetic structures and dynamics from satellite observations in geospace.

Living with urban sounds: Understanding the effects of human mobilities on individual sound exposure and psychological health

People’s exposure to high levels of sound leads to psychological annoyance and stress. This study seeks to understand and conceptualize how human daily mobilities influence urban residents’ sound exposure and psychological health involving annoyance and stress in their everyday lives. Human daily mobilities are understood as people’s daily movement patterns and potentials for movements. Using a mixed-method approach, data were collected from 32 participants in a mixed-housing community in suburban Beijing in China. Each participant carried a portable sound sensor and a GPS tracker and recorded activity-travel diaries for a weekday and a weekend day to track their daily space–time trajectories, measured sound levels, and details of each daily activity and trip. Further, in-depth interviews were conducted to understand participants’ perceptions of urban sounds and psychological health during their daily movements. Geo-narrative analysis was used to integrate these multiple data sources and gain an in-depth understanding of participants’ daily mobilities, individual sound exposures, and perceptions of sound and psychological health. This exploratory study finds that urban residents are exposed to different sound levels and sources in multiple urban geographic contexts in the course of their day. Further, this study identifies how socially vulnerable and susceptible residents encounter difficulties in escaping from high levels of sound in different urban contexts due to their space–time constraints. This study not only enriches the knowledge of how human daily mobilities can influence individual-based sound exposure and psychological health. It also highlights the need to provide better sonic environments for socially vulnerable and susceptible groups in cities.

Data, Disasters, and Space-Time Entanglements

Disasters connected to natural hazards can at the same time be unfolding events, as well as structural phenomena with unequal disaster risk constructed over an extended timespan. Hence, in disaster studies, temporality and spatiality are central, yet often implicit, concepts employed to make sense of the disaster phenomena. In this article we explicitly focus on temporality and spatiality within qualitative disaster studies, particularly those containing ethnographic elements. We use Doreen Massey’s idea of space-time trajectories to analyze and illustrate how in qualitative disaster studies the trajectories of the disaster, research participants, and the researcher entangle in diverse ways. The focus is on how temporality and spatiality are present in the construction of data. The article is mainly conceptual, with illustrations drawn from empirical fieldwork on Valparaíso fire of 2014 in Chile. We interrogate how researchers’ sensitivity to temporality and spatiality challenges the conventional notions and practices of “data” in qualitative disaster studies. The focus in this article is on disaster studies, but it also offers methodological insights to other social sciences that strive to conduct research in the era of “Anthropocene,” with all its shifts and changes, the root causes of which have built over a long time.

De Sitter space as a Glauber-Sudarshan state

Glauber-Sudarshan states, sometimes simply referred to as Glauber states, or alternatively as coherent and squeezed-coherent states, are interesting states in the configuration spaces of any quantum field theories, that closely resemble classical trajectories in space-time. In this paper, we identify four-dimensional de Sitter space as a coherent state over a supersymmetric Minkowski vacuum. Although such an identification is not new, what is new however is the claim that this is realizable in full string theory, but only in conjunction with temporally varying degrees of freedom and quantum corrections resulting from them. Furthermore, fluctuations over the de Sitter space is governed by a generalized graviton (and flux)-added coherent state, also known as the Agarwal-Tara state. The realization of de Sitter space as a state, and not as a vacuum, resolves many issues associated with its entropy, zero-point energy and trans-Planckian censorship, amongst other things.

From Raw Pedestrian Trajectories to Semantic Graph Structured Model—Towards an end-to-end spatiotemporal analytics framework

Abstract The conditions and context in which pedestrians are exposed to the risk of road accidents, air pollution or epidemy are important for improving safety. Spatial information on pedestrian mobility was difficult and expensive to collect so far. This is changing with the popularization of several apps either for guidance or self-monitoring. Produced Space-Time Trajectories (STT) perfectly match the concept of temporal geography, as to assess pedestrian exposure to the above risks. In this article, we propose a modeling approach of pedestrian STT. The abstract model provides a high semantic expressiveness through spatiotemporal queries and a high-level graph representation of the data. We depict a whole framework for collecting and analyzing GPS logs generated by pedestrians’ devices, and discuss the system components. Among the targeted applications, a new generation of mobile applications can be developed that allow pedestrians to organize their daily activities and mobility, and minimize their exposure risks.

Temporal and Spatial Evolution of Passenger Flow in an Urban Rail Transit Network During Station Closure

In this study, we focused on the evolution of passenger flow in an urban rail transit network in both temporal and spatial dimensions under the event of station closure. We constructed an extended space-time-state hyper network so that we could utilize a better-defined three-dimensional solution space to describe passenger behaviors and pedestrian characters. The space-time-state network was extended by adding dummy arcs and setting the “block space-time domain” based on the original spatiotemporal network. Based on the extended space-time-state hyper network, a passenger flow evolution model that aimed to minimize the usage cost during station closure was established considering the strict capacity constraints (including corridor passing capacity, platform load capacity and train transport capacity). For a large-scale urban rail network, we developed a decomposition solution framework in which the Lagrangian relaxation and semi-assignment algorithms were adopted. A real-world instance was implemented based on the Beijing subway network with complete smart card data for each passenger for his/her origin and destination, while the specific space-time trajectories of all passengers and time-dependent passenger volumes in trains and transfer corridors were estimated. The results of a numerical experiment suggest that the proposed passenger flow evolution method can provide a rich set of passenger volume inferences for advanced transit planning and management applications, such as passenger flow control, passenger flow guidance, and real- time train scheduling.

Travel diaries, GPS loggers and Smartphone applications in mapping the daily mobility patterns of students in an urban environment

Abstract Mapping the daily spatial mobility of university students in an urban environment is the focus of this paper. It uses the city of České Budějovice in the Czech Republic as a case study, employing three different research tools – travel diaries, GPS loggers and Smartphone applications. We focus our attention on the analysis of spatial patterns of mobility using basic mobility indicators (distance, number of daily trips, time spent mobility), travel behaviours (use of transport modes) and the detection of time-space bundles (spaces of concentration of particular time-space trajectories) within the city. We identified four main time-space bundles. Then we compare the three main research methods according to their tracking accuracy and informative value. The Smartphone applications (using the A-GPS technology) provided the best results for the spatial mobility of respondents, although the travel diaries method is still unique due to the extent of some socio-demographic and transport characteristics.

Sky‐wave over‐the‐horizon radar simulation tool

This work deals with the entire process of target detection and ranging by a sky-wave over-the-horizon radar (OTHR) computational model simulation. The different processing stages of the transmitted signal along its space–time trajectory from transmission to digital signal processing are modelled. With this simulation tool a moving target present over the sea can be detected according to a set of given initial conditions together with the ionosphere model inputs and the target electromagnetic model. Initial conditions as well as the modulation and filtering options among other parameters of the model can be set easily. The present work is intended to be a further contribution to OTHR studies, providing a user-friendly tool of easy application in order to improve a radar design, facilitate its implementation, as well as for debugging algorithms and signal processing techniques.

The Complex Charge Paradigm: A New Approach for Designing Electromagnetic Wavepackets.

Singularities in optics famously describe a broad range of intriguing phenomena, from vortices and caustics to field divergences near point charges. The diverging fields created by point charges are conventionally seen as a mathematical peculiarity that is neither needed nor related to the description of electromagnetic beams and pulses, and other effects in modern optics. This work disrupts this viewpoint by shifting point charges into the complex plane, and showing that their singularities then give rise to propagating, divergence‐free wavepackets. Specifically, point charges moving in complex space‐time trajectories are shown to map existing wavepackets to corresponding complex trajectories. Tailoring the complex trajectories in this “complex charge paradigm” leads to the discovery and design of new wavepacket families, as well as unprecedented electromagnetic phenomena, such as the combination of both nondiffracting behavior and abruptly‐varying behavior in a single wavepacket. As an example, the abruptly focusing X‐wave–a propagation‐invariant X‐wave‐like wavepacket with prechosen self‐disruptions that enhance its peak intensity by over 200 times–is presented. This work envisions a unified method that captures all existing wavepackets as corresponding complex trajectories, creating a new design tool in modern optics and paving the way to further discoveries of electromagnetic modes and waveshaping applications.

Self-Portraits of Personal Exposure to Air Pollution: on where and when People Are Exposed, and on why it Is Difficult to Avoid

I discuss personal exposure to air pollution through an analysis of the space-time trajectories of seven Brussels residents. Through an activity-based model, I examine how much, when, and where the subjects are exposed to PM2.5 during a typical week. Drawing on social theories of practice, I explore why people become exposed by examining the role of perception and representations of air pollution in organizing a typical week and in considering alternative options. By framing personal exposure as a consequence of the enactment and synchronization of social practices, this research sheds light on how social and ecological processes such as urban planning, energy production, and weather intermingle with the lived experience of individuals and communities to produce specific patterns of pollution exposure. This article is the outcome of a citizen science project conducted in Brussels to test alternative approaches to measure and address outdoor air pollution.